The invention relates to a clamping device for the axial clamping of a tool, especially a disc, on a flange of a driven spindle, and comprising a clamping nut that is screwed on a threaded end shank of the spindle, and a clamping disc arranged between the tool and the clamping nut for biasing the tool against the flange. Clamping devices of this type have proved successful. The advantages afforded thereby are adduced in P 37 05 638. In these devices, the stops against which the rolling bodies, on one hand, and the springs, on the other hand, abut still require relatively complicated and, in terms of their production, expensive parts when provided either on the clamping disc or the clamping nut. These would have to be produced, for example, as sintered parts or extruded parts. However, where sintered parts are concerned, this presents problems for reasons of strength and, as with regards to extruded parts, there is great expense because of the re-working required. Where the supporting bodies rest on the clamping nut and clamping disc and are supported axially, hardened surfaces are desirable in order to reduce the wear and obtain a long lifetime. The hardening of the clamping disc or clamping nut in this region would likewise involve a high outlay and be expensive.